A020528 3rd Bernoulli polynomial evaluated at powers of 2 (multiplied by 6).

0, 18, 252, 2520, 22320, 187488, 1536192, 12435840, 100074240, 802948608, 6433016832, 51501864960, 412165877760, 3297930928128, 26385863196672, 211096568954880, 1688811205754880, 13510644263682048

Offset: 0

Author

Simon Plouffe

Keywords

• nonn

Links

• Index entries for sequences related to Bernoulli numbers.
• Index entries for linear recurrences with constant coefficients, signature (14,-56,64).

Crossrefs

Cf. A016290, A020527.

Programs

Maple

seq(6*bernoulli(3,2^i),i=0..24);

Mathematica

6*BernoulliB[3, 2^Range[0, 30]] (* Paolo Xausa, Sep 16 2024 *)

Formula

a(n) = 3*2^(n+1)*(2^(n+1)-1)*(2^(n+1)-2)/4. - Ralf Stephan, Apr 06 2004

From R. J. Mathar, May 22 2013: (Start)

a(n) = 18*A016290(n-1).

G.f.: -18*x/((8*x-1)*(2*x-1)*(4*x-1)). (End)

a(n) = 14*a(n-1) - 56*a(n-2) + 64*a(n-3). - Wesley Ivan Hurt, Mar 02 2023